Construction of the universal real geometric algebra is well-known, for details see e.g. books [1]}, [2]}, [3]} or paper [4]}. We provide only a brief description in a special case which we are going to use later. In general, geometric algebras are based on symmetric bilinear form of arbitrary signature. Here, we deal with real vector space \(\mathbb {R}^m\)  endowed with a positive definite symmetric bilinear form \(B\)  only.
